Question

Here is the code of binary search tree

#include<stdio.h>
#include<conio.h>
#include"malloc.h"

struct node
{
    int data;
    struct node* left;
    struct node* right;
};
int size(struct node* n)
{
    if(n==NULL)
       return 0;
    else
       return (size(n->left)+1+size(n->right));
}

int maxdepth(struct node* n)
{
    int ldepth,rdepth;
    if(n==NULL)
    {
       return 0;
    }
    else
    {
       ldepth=maxdepth(n->left);
       rdepth=maxdepth(n->right);
       if(ldepth>rdepth)
          return (ldepth+1);
       else
          return (rdepth+1);
    }
}

int lookup(struct node* node,int target)
{
    if(node==NULL)
       return 0;
    else if(target==node->data)
       return 1;
    else if(target<node->data)
       return(lookup(node->left,target));
    else
       return(lookup(node->right,target));
}

struct node* newnode(int data)
{
     struct node* newnod=(struct node*)malloc(sizeof(struct node));
     newnod->data=data;
     newnod->left=NULL;
     newnod->right=NULL;
     return newnod;
}

struct node* insert(struct node* root,int target)
{
    if(root==NULL)
        return(newnode(target));
    else if(target<=root->data)
        root->left=insert(root->left,target);
    else 
        root->right=insert(root->right,target);
    return root;
}

void main()
{
    int result,s,max;
    struct node* newnode=NULL;
    clrscr();
    newnode=insert(newnode,2);
    newnode=insert(newnode,3);
    newnode=insert(newnode,4);
    max=maxdepth(newnode);
    printf("maxdepth %d\n",max);
    s=size(newnode);
    result=lookup(newnode,3);
    printf("size %d\n",s);
    printf("%d",result);
    getch();
}

When I runs this program . I get maxdepth has 3.

If I change the maxdepth function as

int maxdepth(struct node* n)
{
    int ldepth,rdepth;
    if(n==NULL)
    {
        return 0;
    }
    else
    {
        ldepth=maxdepth(n->left);
        rdepth=maxdepth(n->right);
        if(ldepth>rdepth)
            return (ldepth);
        else
            return (rdepth);
    }
}

I get the maxdepth value as 0. what is the problem? I couldn’t not figure it out?

Answer 1

You are not counting the current node, so a +1 is needed.

      {
        ldepth = maxdepth(n->left);
        rdepth = maxdepth(n->right);

        if(ldepth > rdepth)
          return ldepth + 1;
        else
          return rdepth + 1;
      }

Without the +1 maxdepth always will return 0. Because ldepth and rdepth will always be 0.

An example of a tree with 3 nodes:

   A
 /   \
B     C

Now you call maxdepth(A), this will do: ldepth = maxdepth(B); rdepth = maxdepth(C);, then maxDepth(B) will do: ldepth = maxdepth(null); rdepth = maxdepth(null); /* ldepth and rdepth are now 0 */, so maxDepth(B) will return as a result 0. Similar maxDepth(C) will return 0. You will do then:

if(ldepth > rdepth)
  return ldepth;
else
  return rdepth;

But both ldepth and rdepth are 0, so rdepth will be returned which is 0. Finally maxdepth(A) will return 0 as a result.

That’s why +1 is needed.